High-speed nonlinear focus-induced photoresponse in amorphous silicon photodetectors for ultrasensitive 3D imaging applications

A large and growing number of applications benefit from simple, fast and highly sensitive 3D imaging sensors. The Focus-Induced Photoresponse (FIP) can achieve 3D sensing functionalities by simply evaluating the irradiance dependent nonlinear sensor response in defect-based materials. Since this advantage is intricately associated to a slow response, the electrical bandwidth of present FIP detectors is limited to a few \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{kHz}}$$\end{document}kHz only. The devices presented in this work enable modulation frequencies of 700 kHz and beat frequency detection up to at least 3.8 MHz, surpassing the bandwidth of reported device architectures by more than two orders of magnitude. The sensors achieve a SNR of at least \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 53\;{\text{dB}}$$\end{document}∼53dB at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$115\;{\text{cm}}$$\end{document}115cm and a DC FIP detection limit of 0.6 µW/mm2. The mature and scalable low-temperature a-Si:H process technology allows operating the device under ambient air conditions waiving additional back-end passivation, geometrical fill factors of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$100\%$$\end{document}100% and tailoring the FIP towards adjustable 3D sensing applications.

www.nature.com/scientificreports/ demonstrated in various thin-film devices 13,14 that obtain a significant density of states within the bandgap, such as organic solar cells or lead sulfide (PbS) photoconductors. As demonstrated in 13 , the read-out of two analogue sensor outputs at different focus spot positions enables: (I) Maximum scalability (100% FF) since the depth information can directly be extracted from the detected FIP signal from a single viewpoint, (II) Highly precise distance measurements with depth resolutions of ± 0.1% at 51.8 cm as well as long-range distance measurements up to at least 72 m , and (III) Low-light level detection at irradiances down to 10 µW/mm 2 in the visible range.
Although the FIP technique combines several advantages, its true benefit can only be achieved at high frequencies which enables the observation of fast moving objects and significantly reduces flicker noise, hence increasing the signal-to-noise ratio (SNR). Unfortunately, the cut-off frequency of state of the art sensors is presently limited to a few kHz 18 , only.
High defect densities and low charge carrier mobilities limit both, the bandwidth and responsivities in state of the art reported FIP detectors 13,14 . Physical phenomena leading to the FIP, differ significantly depending on the device architecture, the mode of operation and most importantly the material compositions and qualities.
In 13 , the FIP has been reported in highly complex dye sensitized solar cells (DSSC), whose fabrication requires additional back-end passivation to avoid moisture-and oxygen induced performance degradation. Here, trapping and de-trapping of photo-generated charge carriers in localized defect states increases the electron diffusion in a mesoporous TiO 2 layer with increasing electron concentrations 13,19 . Depending on irradiance levels, the FIP in solar cells can be attributed either to charge carrier trapping decreasing responsivities at low intensities 20,21 or to recombination resulting in series resistance variations when incident light intensities exceed one sun 22 . Alternatively, the FIP in post-encapsulated PbS photoconductors can be assigned to local resistivity changes 13 . PbS photoconductors are opaque prohibiting large-scale integration as single pixel sensor stacks. The organic photodetectors (OPD) proposed in 18 also require an additional passivation and utilize a complex multilayer structure to form internal energetic barriers that screen the electric field for different irradiances causing the FIP.
In this paper, we report a high-speed detector design utilizing a well-established, low-temperature technology which significantly surpasses the bandwidth of all previously reported FIP sensor designs. The following section discusses the device technology and physics. The subsequent section presents experimental distance measurement results along with a primarily proposed sensor read-out technique based on a harmonic analysis.

Device technology and physics
For the first time, we used an amorphous silicon PIN photodiode for FIP. This diode has been specifically designed to optimize the nonlinear irradiance photocurrent detection. Compared to previously reported FIP detectors, the technology and fabrication of hydrogenated amorphous silicon (a-Si:H) photodiodes is simple, mature, scalable and suitable for back end of line device integration with traditional complementary metal-oxide-semiconductor (CMOS) electronics. Beyond that, this technology enables geometrical fill factors of 100% 23,24 and allows precise, application specific tailoring of the FIP. A significant advantage compared to the former architectures is that a-Si:H FIP sensors do not require an additional passivation and can easily be operated under ambient air conditions. Besides technological benefits, an additional advantage of a-Si:H towards state of the art organic and dye-sensitized devices is the long-term stability, which is a fundamental requirement for an image sensor pixel 25,26 . We first investigate an irradiance dependent current breakdown in a-Si:H photodetectors systematically by electro-optical simulations. Next, a-Si:H FIP sensors have been fabricated via plasma enhanced chemical vapor deposition (PECVD) and characterized electro-optically to validate fundamental device functionalities and reliability. Z-Scan current measurements have been performed to study the influence of the irradiance and the bias voltage on the FIP. The z-Scan technique is a well-established and widely acknowledged method to precisely quantify and characterize optical nonlinearities in solids, liquids, or solutions 27 . We adapt this technique and develop a comprehensive electro-optical simulation model of irradiance dependent current measurements on a-Si:H FIP detectors utilizing the software AFORS-HET 28 . Finally, we demonstrate AC distance measurements based on the optimized FIP sensor design for different modulation frequencies. Details about the deposition tool, process parameters, simulation procedures and the measurement setups are given in the Methods and the Supplementary Information.
Electro-optical simulations. The simulation results enable systematic investigations on internal charge carrier statistics and transport processes and serve as input parameters for subsequent fabrication steps.
Electro-optical simulations of the complete ITO-PIN-ITO multilayer stack have been conducted at a wavelength of 488 nm for different photon fluxes of 0 = 0 , 1 = 10 14 cm −2 s −1 , 2 = 10 16 cm −2 s −1 and 3 = 10 18 cm −2 s −1 , respectively. The corresponding irradiances and detector positions in the z-Scan are given in the Supplementary Information. A bias voltage V bias of 0 V has been used to prevent bias induced band bending and influences on the intrinsic electric field E i . www.nature.com/scientificreports/ Here, the built-in voltage V bi depends on the mobility gap energy E M and on E F(n,p−layer) that is the energetic distance between the Fermi levels of n-/p-type a-Si:H and the corresponding mobility edges 29 . Acceptor doping concentrations of N a = 6 · 10 19 cm −3 for the p-layer and donor doping concentrations of N d = 5 · 10 19 cm −3 for the n-type a-Si:H serve as input parameters for the simulations. These values have been calculated taking into account the atomic density of a-Si:H 30 and appropriate literature on a-Si:H technology 29 considering specific deposition process parameters. Bias dependent z-Scan results confirm 0 V to be the optimal device specific operation condition (cf. Fig. S4) for enhanced 3D depth sensing applications. To the best of our knowledge, bias tunable FIP detectors have not been reported by other groups before 13,14 .
The simulations that are discussed in the following help to identify the physical origin of the FIP in a-Si:H PIN photodiodes. They reveal a huge variety of depth and irradiance dependent device parameters, including charge carrier generation and recombination processes and local current densities. In the following, we discuss three particular characteristics: (I) Band profiles including the quasi Fermi energies for electrons E fn and holes E fp , (II) Charge carrier densities ∼ = charge carriers being trapped in defect states Q tr , and (III) Electric field profiles. Figure 1a-b shows simulated bandgap profiles across the intrinsic absorption layer for different irradiance levels. Under illumination, the Fermi energy E F splits into the quasi Fermi energies E fn and E fp . These energy levels bend due to charge carrier injection, with E fn converging towards the conduction, E fp towards the valence band tail. Furthermore, the hole concentration h + in the device front increases moderately. However, the concentration of electrons e − significantly increases at higher irradiance levels, as shown in the charge carrier statistics (cf. Fig. 1c-d). This coincides with E fn having local convergence more intensely towards the conduction tail edge than E fp to E V ,tail (cf. Fig. 1e). The position x i where the majority carrier type changes from h + to e − , shifts towards the light incident side at higher irradiances ( Fig. 1c-d). In the dark state 0 , as well as at the low and moderate irradiances of 1 and 2 , defect states Q tr are positively charged (solid lines) close to the p-type region, while they are negatively charged (dashed lines) close to the rear contact. Both parameters, x i and Q tr play a significant role to understand the FIP, as they determine the electrical field profile and charge carrier transport mechanism within the device. Without illumination, the majority carrier distribution of h + and e − is almost symmetric (cf. Fig. 1c) and hence the detector retains a uniform electric field across the intrinsic layer (i-layer) as predicted by Crandall considering material and device specific assumptions 31 (cf. Fig. 1f). Furthermore, in equilibrium, electrons are able to drift to the rear contact due to the built-in field. At high intensity illumination 3 , the e − concentration at the light incident side surmounts that of h + leading to a change in the majority carrier type. In addition, throughout the complete intrinsic region, the relationship E C − E fn < E fp − E V is maintained and hence all defect states Q tr become negatively charged. This irradiance dependent defect charging influences the local electrical field (cf. Fig. 1f) and charge transport significantly, leading to a complete field collapse or even field reversal at higher fluences. Further details on internal device physics are given in 32 .
Since the electric field at the PI-interface of the PIN photodiode becomes positive, a significantly large amount of trapped and free e − is not able to penetrate further, resulting in a total negative space charge ρ throughout the complete absorbing region. Using Poisson's equation with the electric field E , and the relative permittivity of a-Si:H ε a−Si:H the negative space charge extenuates and quenches the electric field at the rear end of the device. The partial rise to potentially even positive E-field at the device front disturbs and-particularly in case of a field reversal-prevents charge to be collected efficiently. As a result, the total device current decreases. From the simulation results, we systematically extracted process parameters (cf. Supplementary Information) required for low temperature a-Si:H FIP detector fabrication.

Distance measurements utilizing a-Si:H FIP sensors
Experimental setup. The hypothesis of a significant E-field distortion within the FIP sensor quenching the total device current at high irradiances in the simulation coincides with the experimental z-Scan current measurement as presented in the Supplementary Information. We observe a significant current breakdown, once the a-Si:H thin-film detector is placed in focus of a 488 nm laser beam with a total power ≤ 150 µW. Compared to state of the art FIP sensors 13,14 , the FIP in a-Si:H samples occurs at irradiances down to at least 0.6 µW/mm 2 far out of focus (cf. Supplementary Information). This surpasses cutting-edge benchmarks by at least a factor of 16 in the visible range. Such irradiances can easily be achieved utilizing flashlights or light emitting diodes, removing the need of expensive laser technology. Both, simulation results and experimental findings verify that the high charge carrier densities locally reduce the internal electrical field in the device, resulting in an irradiance dependent current breakdown and hence enabling via this sensitive nonlinearity optical distance measurements as elaborated in 13 .
The FIP in a-Si:H has been exploited and performance limits investigated for optical distance measurements at various modulation frequencies f mod , a wavelength of 477 nm , 0 V bias and distances exceeding 1 m . A schematic of the setup for optical measurements is shown in Fig. 2. Initially, the single-pixel FIP sensor has been placed in focus at a specific distance d . The diverging lens converts a collimated laser beam into a radial emitter. The www.nature.com/scientificreports/ converging lens then focuses the collected photons on the detector. Compared to previous reports, we propose an alternative FIP sensor readout to extract ultrasensitive distance information instantaneously from the incident light by applying a Fast Fourier Transform (FFT) on the sensor output at different distances. This novel approach based on a harmonic analysis allows for single-pixel distance determination, whereas previous concepts invariably relied on two separate FIP sensors and a signal comparison of two detector outputs 13,14,18 . The proposed sensor readout in this work can easily be integrated on-chip, e.g. by embedding two narrow bandpass filters for signal acquisition at two specific measurement frequencies and a current/voltage divider circuit to determine signal quotients for unambiguous distance determination. Hereby, the low-temperature a-Si:H deposition technique  Fig. 3a. The normalized absolute FFT signals are given in Fig. 3b. While the rectangular shape of the modulation is clearly visible at the sensor output, further overshoots occur at the rising and falling signal edges as a result of photo-induced storage charges in illuminated a-Si:H PIN photodiodes 33 . These signal overshoots in the time domain can be explained by a slow filling and discharging of trapping states, predominantly of deep dangling bond states 34,35 . Although frequency domain a-Si:H photodiode signals already have been studied extensively in the past, anomalies besides the typical harmonic frequencies have not been reported, yet 33 . Conventional low-defect monocrystalline silicon (c-Si) photodetectors (S1337-33BQ, Hamamatsu) neither show significant capacitive (de-)charging in the time domain, nor a beat frequency generation in the frequency domain (cf. Fig. 3b). In order to maximize the sensor sensitivity, we conducted frequency dependent distance measurements as the 1/f noise in a-Si:H PIN photodiodes can be reduced significantly at higher frequencies 36 . For this, it is important to determine the RC time-constant of the  14 . At the position d = 142 cm , the sensor is placed in focus since the FFT signals increase for shorter distances due to the FIP. Besides the expected harmonics at the frequency positions ξ = (2 · n + 1) · f mod , additional beat frequencies occur in the frequency spectrum at � = (2 · n) · f mod . The normalized FFT amplitudes are given in Fig. 3d showing the frequency spectrum covering 600 kHz up to 2.2 MHz . Here, the nonlinear current breakdown can be verified clearly at 2.1 MHz enabling unambiguous distance determination up to that frequency range by comparing signal amplitudes at the frequency positions and ξ.
We further analyzed the time domain sensor signal at f mod = 200 kHz to study the beat frequencies origin, their evolution, and, most importantly the sensor sensitivity at a specific distance and frequency below f c (cf. Fig. 4a). In the first step, the defect-induced overshoot has been separated from the idealized rectangular detector output that has been fitted considering the steady-state current values (cf. Fig. 4b). The difference between the detector current and the fitted rectangular in the time domain is shown in Fig. 4c. The corresponding frequency domain signals are given in Fig. 4d. While the a-Si:H detector output obtains significant beat frequencies at the positions f beat = (2 · n) · f mod , the FFT amplitude of the rectangular signal vanishes by definition at these spot frequencies (cf. Fig. 4d). These measurement results unambiguously verify that the defect-induced signal overshoots in the time domain can be identified to be the origin of additional beat frequencies. This can easily be exploited for enhanced, high-sensitivity optical distance measurements by measuring peak amplitudes at or ξ relative to f mod for various distances. In order to achieve high sensitive distance measurement, it is important www.nature.com/scientificreports/ to evaluate the optimum modulation ( f mod ) and measurement ( f meas ) frequency to maximize the SNR, hence the sensors sensitivity.
Signal-to-noise. Figure 5a shows the normalized absolute FFT signals for a rectangular modulation of f mod = 200 kHz at d = 115 cm and d = 142 cm and 0 V bias. At 142 cm , the sensor is placed in focus. A reliable distance distinction up to at least ξ = 3.8 MHz for f mod = 200 kHz is possible (cf. Fig. 5b). This surpasses existing benchmarks of complex dye-sensitized solar cell FIP sensors far more than three orders of magnitude in the visible range 13,14,18 . Measuring peak amplitudes at two different frequency positions n · f mod ∧ m · f mod ; n � = m; n, m � = 0 not only allows for a fast distance determination and distinction, but also increases the SNR at higher measurement frequencies since the 1/f noise in a-Si:H PIN photodiodes can be reduced significantly at higher frequencies 36 . A significant SNR improvement from ∼ 15 dB to ∼ 53 dB at 200 kHz reveals Fig. 5c-f. Since the FIP detector response is RC-limited, the SNR decreases at its maximum modulation of f mod = 700 kHz compared to f mod = 200 kHz . The high SNR values throughout the complete frequency spectrum for 200 kHz modulation consistently indicate that the irradiances can be further decreased significantly in futures distance measurement experiments.

Depth resolution.
To further estimate the achievable depth resolution d of this device specific single sensor readout approach and to eliminate influences of the total light power as shown in Fig. 2, we further define a FIP detector current ratio for two different measurement frequencies In Fig. 2 (bottom), the distance dependent evolution of this ratio is exemplarily shown for the 1st nonlinear beat frequency f 1 = fˆ 1 = 1 MHz and a modulation nearby the sensors cut-off frequency f 2 = f mod = 500 kHz . The maximum relative deviation of this ratio corresponds to the achievable depth resolution at a specific distance. Fitting the signal curvatures slope with a linear regression results in ± 0.167% precision at a distance of d = 1.255 m , that corresponds to a depth resolution of d = 2.09 mm . Achieving ± 0.167% precision coincides  www.nature.com/scientificreports/ with results previously reported in 13 , but at far more than twice the distance verifying significant performance improvements and potentials of this highly sensitive amorphous silicon based sensor approach and read-out concept. We believe further improvements on the bias and irradiance dependent current breakdown in a-Si:H photodiodes can be achieved in the future by optimizing: (I) Intrinsic sensor parameters (thin-film architecture and composition), (II) Extrinsic operation parameters (sensor bias, wavelength and modulation), and (III) Optics (focal length, numerical aperture).
A performance comparison between state of the art FIP detectors and the results achieved and reported in this work are given in Table 1. www.nature.com/scientificreports/

Conclusion
The bias and irradiance dependent current breakdown in a-Si:H PIN photodiodes has been investigated systematically by electro-optical simulations and utilized for optical distance measurements. The FIP can physically be explained by electric field screening within the intrinsic layer due to defect-assisted charge carrier trapping. We identify a local and irradiance dependent reversal of the electrical field due to localized occupied trapping states. The field reversal quenches the drift region for electrons drastically and limits the charge carrier transport at higher intensities. The a-Si:H FIP sensor and the primarily proposed read-out based on harmonic analyses enable measuring distances at modulation frequencies up to of 700 kHz , beat frequency detection up to at least 3.8 MHz at a distance of at least 1.42 m , and depth resolutions down to 2.09 mm . At 200 kHz , we achieve a maximum SNR of ∼ 53 dB . At continuous wave illumination, the a-Si:H FIP sensor exhibits a detection limit of at least 380 nW , corresponding to an irradiance of 0.6 µW/mm 2 . Utilizing the flexible, low-temperature and mature PECVD technology, sensor architectures and material compositions can further be developed towards fast, highly sensitive long-range distance measurements. Since the a-Si:H device fabrication is reproducible, scalable and allows for sensor integration on top of silicon electronics with fill factors of 100% , this approach enables significant performance improvements of 3D imaging systems compared to existing technologies.

Methods
Device fabrication. A-Si:H PIN photodiodes were grown onto glass substrates in a conventional plasmaenhanced CVD (PE-CVD) process in a MVS multi-chamber vacuum system at substrate temperatures below 300 • C . Anode and cathode contacts made of indium tin oxide (ITO) were deposited in a hot-wall radio-frequency sputtering system at temperatures below 50 • C . Subsequent to these depositions, all devices have been thoroughly cleaned, structured by contact UV-lithography, packaged and contacted via semi-automated wedge bonding. The Supplementary Information provides further fabrication details. To characterize thin film layer thicknesses, deposition homogeneity and reproducibility, measurements utilizing a FEI Quanta 250 environmental scanning electron microscope (ESEM) have been performed on the devices in a nitrogen atmosphere. An ESEM measurement of the TCO-PIN -TCO multilayer stack is exemplarily shown in Fig. 6. Prior to these analyses, cross-sections of the devices have been prepared with a FEI Helios NanoLab600 focused ion-beam (FIB). The total device thicknesses have also been validated by a Bruker Dektak XT profilometer. www.nature.com/scientificreports/ Simulations. Electro-optical simulations of the z-Scan current measurement utilize a Gaussian beam profile to determine the spot size and the total photon flux on the detector serving as input parameters for the AFORS-HET simulation software 28 . To calculate the total sensor current, the simulation model takes the illuminated and dark detector areas into account. Further details are given in the Supplementary Information.

Distance measurements. Modulated distance measurements have been performed using an Omicron
LDM473.20A350 laser with a peak wavelength of 477 nm . The power on the detector has been determined by a crystalline silicon reference detector. Utilizing the technique described in the Supplementary Information of 13 , the optical power on the sensor of 7.6 mW corresponds to an irradiance of ∼ 2 · 10 18 cm −2 s −1 . The incident photons have been guided through a diverging lens with a focal length of 30 mm to generate a light cone similar to that of a homogenous emitting object. A lens with a focal length of 160 mm has been used to focus the beam on the sensor, which has been positioned at variable distances behind the lens. The detector current has been converted to a voltage and amplified using a FEMTO DHPCA 100 I-V converter. Transient and FFT signal acquisition has been realized with a Tektronix TDS 3034C digital oscilloscope exhibiting a bandwidth of 300 MHz and 2.5 GS/s . The signals have been recorded as an envelope of 512 measurements. Depth resolution measurements utilize a 444 nm laser light source with an optical power on the sensor of 4.1 mW.

Data availability
Data available on request from the corresponding author.